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1999. 221p. This fascinating book is the most popular, simple and direct introduction to rapid geometry techniques and calculations developed from Vedic Maths, a popularized version of "Geometry For an Oral Tradition", listed below. It is a delightful read which will completely reorientate one's vision and understanding of Geometry within as little as a few hours. The approach is ideally suited to the twenty-first century, when audio-visual forms of communication are likely to be dominant. Contents: Angles, Triangles & Quadrilaterals; Properties of a Circle; Multiplication & Area; Parallels & Parallelograms; Similar Triangle' Equality & Equations; Number Arithemetic, Geometry & Algebra; Equal Areas & Similar Triangles; Further Properties of Circles; Pythagoras' Theorem; Proportion.

1999. 130 Large pages. Inspired by Vedic Maths and Euclid, this book presents direct, immediate and easily understood geometric proofs. These proofs are based on only one assumption (that magnitudes are unchanged by motion) and three additional provisions (a means of drawing figures, the language used and the ability to recognize valid reasoning). Starting from these first principles it leads to theorems on elementary properties of circles.. It includes discussion on the relevant philosophy of mathematics and is written both for mathematicians and for a wider audience. Contents: Introduction; Preliminaries; Provisions; Definitions; PROPOSITIONS; Part A: Congruence, Magnitudes and Lines; Part B: Angles, Parallels, Triangles And Quadrilaterals; Part C: Concerning ;Area Equalities And Similar Triangles Part D: Elementary Properties Of A Circle; COMMENTARY: Part I: Some Basics; Part II: Language And Reason; Part III: Comparisons With Euclid's Elements; Par IV: Movement In Geometry; Part V: The Valid Use Of Figures; Summary And Conclusions; References; APPENDICES: Appendix 1: Application Of The Sixteen Sutras To The Present System Of Geometry; Appendix 2: Alternative Proofs And Sequences In Part D; Appendix 3: Further Definitions.

Discover Vedic Mathematics: A Practical System Based on Sixteen Simple Formulae.Kenneth R. Williams

2004. 210 Large P. This book shows how the Vedic Maths system applies in a large number of areas of elementary mathematics, covering arithmetic, algebra, geometry, calculus etc. Each chapter concentrates on one Vedic Sutra or Sub-sutra and shows many applications. This gives a real feel for the Vedic Sutras each of which has its own unique character. It covers much of the content of Bharati Krishna's book above but in more detail and with more applications and explanations. It also contains Vedic solutions to GCSE and 'A' level examination questions. Preface; Illustrative Examples; 1 All From Nine And The Last From Ten; 2 Vertically And Crosswise; 3 Proportionately; 4 By Addition And By Subtraction; 5 By Alternate Elimination And Retention; 6 By Mere Observation; 7 Using The Average; 8 Transpose And Apply; 9 One In Ratio- The Other One Zero; 10 When The Samuccaya Is The Same It Is Zero; 11 The First By The First And The Last By The Last; 12 By The Completion Or Non-Completion; 13 By One More Than The One Before; 14 The Product Of The Sum Is The Sum Of The Products; 15 Only The Last Terms; 16 Calculus; 'O' And 'A' Level Examination ;Papers; List Of The Vedic Sutras; Index Of The Vedic Formulae; Answers To Exercises; Index.

The Natural Calculator: Using The Natural Processes Of The Mind For Mental Calculations.Kenneth R. Williams

2004. 102 Pages. In this book the emphasis is on mental calculation, mainly mental multiplication, but addition, subtraction and division are also covered. Each chapter focuses on one Vedic formula and shows various ways in which it can be used. There is a detailed introduction outlining the benefits of mental mathematics(Vedic Maths). Introduction; 1 On The Flag Calculating From Left To Right; 2 Proportionately Multiplication Devices Involving Doubling And Halving; 3 By One More Than The One Before Squaring Numbers That End In 5; A Special Type Of Multiplication; 4 The First By The First And The Last By The Last Calculating Checks; A Special Type Of Multiplication; 5 All From 9 And The Last From 10 Numbers Near A Base; Subtraction; Numbers Near Different Bases; Multiplying Three Numbers Simultaneously; Squaring Numbers Near A Base; Multiplication By 9's; Addition And Subtraction; 6 Vertically And Crosswise General Multiplication: Multiplying 2-Figure Numbers, 3-Figure Numbers, Moving Multiplier Method, 3 And 4-Figure Multiplication; General Squaring; Division- Divisor Near A Base; General Division; 7 Using The Average Products Using An Average; 8 By Addition And By Subtraction Squares From Squares; Products From Products; 9 By Mere Observation Use Of Special Numbers; Proofs; References; Answers.

2004. 200P. This is an advanced book of sixteen chapters on one Vedic Maths Sutra, “Vertically & Crosswise”, ranging from elementary multiplication, etc. to the solution of non-linear partial differential equations. It deals with (i) calculation of common functions and their series expansions, and (ii) the solution of equations, starting with simultaneous equations and moving on to algebraic, transcendental and differential equations. The text contains exercises and answers. Contents: 1 Introduction To The Vertically And Crosswise Sutra; 2 Combined Operations Of Elementary Arithmetic; 3 Evaluation Of Determinants; 4 The Solution Of Simultaneous Linear Equations; 5 Inversion Of Matrices; 6 Curve-Fitting; 7 Evaluation Of Logarithms And Exponentials; 8 Change Of Roots Of Equations; 9 Sine, Cosine And Inverse Tangent; 10 Inverse Sine And Cosine And Tangent; 11 Transcendental Equations; 12 Solution Of Cubic And Higher Order Equations; 13 Functions Of Polynomials; 14 Functions Of Bipolynomials; 15 The Solution Of Linear And Non-Linear Differential, Integral And Integro-Differential Equations; 16 The Solution Of Linear And Non-Linear Partial Differential Equations.

1998. 250+ Large P. Each of the three books has 27 chapters each of which is prefaced by an inspiring quote from a famous mathematician, philosopher etc. Also in each book there are historical notes which relate to the authors of the quotes, a list of Sutras and three other short but interesting sections (e.g. Pascal's Triangle,Vedic Maths, Fractals). Written for 11-14 year old pupils (some of the material in Books 1 and 2 is suitable for children from the age of about eight) this course covers the National Curriculum for England and Wales, but is also the perfect course for anyone who wants to develop a thorough understanding of Vedic Mathematics. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 1 deals mainly with basic arithmetic, proportion, decimals, basic algebra and geometry, polygons, area, volume etc. For detailed contents see the Expedient Learning Portal.

1990. 171P. This legendary book was first published in English in 1990. It is Altshuller's most popular book in Russia on how to become an inventor and how to solve technical problems. Originally written for high school students, it engages readers of all ages by inviting them to learn by doing. The translator, Lev Shulyak, is himself an accomplished inventor, engineer and TRIZ expert. About the Author: Genrich Altshuller received his first Soviet patent at the age of 14. While in his early 20s, he began developing TRIZ, the Theory of Inventive Problem Solving. Stalin rewarded him with 25 years imprisonment in Siberia. Released after Stalin’s death, he led the underground TRIZ revolution, a fundamental shift in the technical creativity paradigm. Altshuller spent the remainder of his life working to advance what has become the science of TRIZ. He died in 1998. The similarity between many of these techniques and Vedic Mathematics is striking, particularly considering that both authors developed their systems around the same time period.

3 Volumes, Teachers Guide, & Answer Book. This is cheaper paper edition of the Cosmic Computer published by Motilal Banarsidass & imported from India. Best suited for teacher’s use in a classroom setting with guide & answers in separate volume. Written for 11-14 year old pupils (some of the material in Books 1 and 2 is suitable for children from the age of about eight) this course covers the National Curriculum for England and Wales. The full course consists of three Textbooks, one Teacher's Guide and one Answer Book for all 3 volumes. THE TEXT BOOKS Each of the three books has 27 chapters each of which is prefaced by an inspiring quote from a famous mathematician, philosopher etc. Also in each book there are historical notes which relate to the authors of the quotes, a list of Sutras and three other short but interesting sections (e.g. Pascal's Triangle, Fractals). Book 1 deals mainly with basic arithmetic, proportion, decimals, basic algebra and geometry, polygons, area, volume etc. Book 2 extends this, covering fractions, probability, sequences, negative numbers, percentages, equations, graphs, charts, transformations, bearings etc. Book 3 develops this further into recurring decimals, square and cube roots, division, divisibility, the musical scale, formulae, simultaneous equations, quadratic equations, proof, similar triangles, area of a circle, nets, conic sections, loci, motion, vectors, Pythagoras' theorem, triples, coordinate geometry etc. THE TEACHER'S GUIDE Contains A Summary of the book. A copy of the Unified Field Chart for that book. Notes on the content of the chapters- advice, suggestions etc. Mental Tests (correlated with the books) and answers- which allow earlier work to be regularly revised, give stimulating ideas relevant to the current lesson and which develop themes from earlier tests which may ultimately become the subject of a lesson. Extension Material and answers (about 16 per book)- these consist of a 1 or 2-sided sheet given to children who work fast and get ahead of the rest of the class. Many of these are also very suitable for work with a whole class. Revision Tests and Answers- There is a revision test every 4 or 5 chapters. This includes a mental test of 10 questions. Games, Worksheets etc. THE ANSWER BOOK This contains answers to all exercises and other numbered questions in the text and should be available for pupils during lessons.

2005. Contents:PREFACE;LESSON 1 COMPLETING THE WHOLE;Introduction The Ten Point Circle; Multiples of Ten; Deficiency from Ten; Deficiency and Completion Together Mental Addition; Completing the Whole; Columns of Figures; By Addition and By Subtraction; Subtracting Numbers Near a Base; LESSON 2 DOUBLING AND HALVING: Doubling; Multiplying by 4, 8 Halving; Splitting Numbers; Dividing by 4, 8; Extending your Tables; Multiplying by 5, 50, 25 Dividing by 5, 50, 25; Dividing by 5; Dividing by 50, 25; LESSON 3 DIGIT SUMS: Adding Digits; The Nine Point; Circle; Casting out Nines; Digit Sum Puzzles; More Digit Sum Puzzles; The Digit Sum Check Multiplication Check; The Vedic square; Patterns from the Vedic Square; Number Nine; LESSON 4 LEFT TO RIGHT: Addition: Left to Right; Multiplication: Left to Right; Doubling and Halving; Subtraction: Left to Right; Checking Subtraction Sums; More Subtractions; LESSON 5 ALL FROM 9 AND THE LAST FROM 10: All From 9 and the Last from 10; Subtraction Adding Zeros; One Less; One More; One Less Again; Money LESSON 6 NUMBER SPLITTING: Addition; Subtraction; Multiplication; Division; LESSON 7 BASE MULTIPLICATION: Times Tables; Numbers just Over Ten; Multiplication Table Patterns; Recurring Decimals; Numbers Close to 100; Mentally; Numbers Over 100 Mental Maths; Russian Peasant; Multiplication; Larger Numbers; Numbers Above the Base; Proportionately; Another Application of Proportionately; Multiplying Numbers near Different Bases; Squaring Numbers near a Base; A Summary. LESSON 8 CHECKING AND DIVISIBILITY Digit Sum Check for Division The First by the First and the Last by the Last The First by the First The Last by the Last Divisibility by 4 Divisibility by 11 Remainder after Division by 11 Another Digit Sum Check LESSON 9 BAR NUMBERS Removing Bar Numbers All from 9 and the Last from 10 Subtraction Creating Bar Numbers Using Bar Numbers LESSON 10 SPECIAL MULTIPLICATION Multiplication by 11 Carries Longer Numbers By One More than the One Before Multiplication by Nines The First by the First and the Last by the Last Using the Average Special Numbers Repeating Numbers Proportionately Disguises LESSON 11 GENERAL MULTIPLICATION Revision Two-Figure Numbers Carries Moving Multiplier Extension Multiplying Binomials Multiplying 3-Figure Numbers Written Calculations LESSON 12 SQUARING Squaring Numbers that end in 5 Squaring Numbers Near 50 General Squaring The Duplex Number Splitting Algebraic Squaring Digit Sums of squares Square Roots of Perfect Squares 3 and 4 Figure Numbers LESSON 13 EQUATIONS One-step Equations Two-step Equations Three-step Equations LESSON 14 FRACTIONS Vertically and Crosswise A Simplification Comparing Fractions Unification of Operations LESSON 15 SPECIAL DIVISION Division by 9 Longer Numbers Carries A Short Cut Division by 8 etc. Division by 99, 98 etc. Divisor Below a Base Number Two-Figure answers Divisor Above a Base Number LESSON 16 THE CROWNING GEM Single Figure on the Flag Short Division Digression Longer Numbers Negative Flag Digits Decimalising the Remainder; SUTRAS AND SUB-SUTRAS;9-POINT CIRCLES; REFERENCES;INDEX OF THE VEDIC FORMULAE;INDEX.